Stability of isometric maps in the Heisenberg group
Nicola Arcozzi, Daniele Morbidelli
Abstract
In this paper we prove some approximation results for biLipschitz maps in the Heisenberg group. Namely, we show that a biLipschitz map with biLipschitz constant close to one can be pointwise approximated, quantitatively on any fixed ball, by an isometry. This leds to an approximation in BMO norm for the map's Pansu derivative. We also prove that a global quasigeodesic can be approximated by a geodesic in any fixed segment.
Create a lesson
Related papers
On the geometry of real polynomials of the 7-th degree with simple complex critical points
Elizaveta Khokhlova, Yury Kochetkov
Uniqueness of the hexagonal lattice's universal optimality
Markus Faulhuber, Philipp Petersen
Hadamard configurations and sharp cubic-period bounds for stealth in dimensions 10, 11, and 12
Josiah Park
Scaling Limits and Fractal Dimensions of ω-Substitution Graph Systems
Qingcheng Zeng, Yumei Xue, Cheng Zeng
Filling Lipschitz spheres in metric spaces
Noa Vikman, Stefan Wenger
Logarithmically Slim Polygons
Panagiotis Tselekidis